Question: Cisco Systems, Inc., is the leading maker of networking gear that connects computers to the Internet. Company managers are concerned with the productivity of their workers as well as their job satisfaction. Kate D'Camp is the senior vice president for human resources. She often initiates surveys concerning Cisco's personnel. A typical survey asked, "Do you feel it's OK for your company to monitor your Internet use?" Of the 405 respondents, 223 chose "Only after informing me." Cisco would consider monitoring if more than 50% of its workers wouldn't mind if informed beforehand that the company was going to monitor their Internet usage.

a. D'Camp may have read the USA Today issue that indicated 55% of American workers wouldn't object after being informed. So she might desire that the test indicate with a high probability that more than 50% of Cisco workers wouldn't object when in fact her workers reflect the opinion of all American workers. Calculate the probability that this would be the case.

b. Conduct the procedure to determine if the proportion of workers who wouldn't object to the company monitoring their Internet use after they were informed is more than 50%. Use a significance level of 0.05.